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Abstract

The solvability of the nonlocal boundary value problem $$\begin{gathered} u_t = a(t,x,u,u_x )u_{xx} + b(t,x,u,u_x ),{\text{ }}0 \leqslant t \leqslant T,{\text{ }}\left| x \right| \leqslant l, \hfill {\text{ }}u(0,x) = 0,{\text{ }}u(t, - l) = u(t,l),{\text{ }}u_x (t, - l) = u_x (t,l) \hfill \end{gathered}$$ in a class of functions is investigated for a quasilinear parabolic equation. The solution uniqueness follows from the maximum principle.

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DOI

10.1023/a:1022972616163

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